CAT Practice : Speed Time, Races

Distance betw A and B

    Q.24: Two persons A and B start moving at each other from point P and Q respectively which are 1400 Km apart. Speed of A is 50 Km/hr and that of B is 20 Km/hr. How far is A from Q when he meets B for the 22nd time?
    1. 1000 Km
    2. 400 Km
    3. 800 Km
    4. 1400 Km


  • Correct Answer
    Choice B.400 Km

Detailed Solution

Total distance travelled by both of them for 22nd meeting = 1400 + 21 x 2 x 1400 = 43 x 1400

Distance travelled by each will be in proportion of their speed:-

Therefore, distance travelled by A = 50/(50 + 20) x 43 x 1400 = 43000 (Note - Always do complicated calculations at last because things cancel out generally)

Now, for every odd multiple of 1400, A will be at Q and for every even multiple of 1400 A will be at P. So, at 42000 Km (1400 x 30, even multiple) A will beat P. So at their 22 meeting, A will be 1000 Km from P, therefore, 400 Km from Q.

Correct Answer: 400 Km

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More questions from Speed Time, Races

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  8. Relative Speed
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"Life is a race ... if you don't run fast ... you will be like a broken undaa" - Veerusahasra Buddhi